You should pay attention on whether the graphic designer candidate is an expert in print graphics or stuff on the screen. I've seen designers that design great milk cartons but just simply awful website layouts. Apart from that, it's of course a matter of taste; if you like the designer's work or not.
Then there are the basic terms that apply to seeking resources (hiring new employees or consultants), but one of the most important ones here is whether the designer is likely to get things done. This is because graphic design is a creative job and relies highly on inspiration and motivation.
This is of course hard to find out if you don't actually know the person in question, but a good basic principle is to hire some one who actually does this for his living. I've found myself struggling with brilliant amateur artists that just can't get anything done, 'cause it's all time spent away from their own hobby projects. Professional graphic designers are more likely to find the time to get into the zone for Your assignment.